Details

sample223.0ms

Algorithm

intervals

Results

33.0ms	210×	body	80	valid
24.0ms	28×	body	2560	valid
18.0ms	27×	body	1280	valid
14.0ms	98×	body	80	nan
7.0ms	13×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	1×	body	160	valid

simplify113.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

112.0ms

(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize38.0ms

Local error

Found 4 expressions with local error:

20.2b	(sqrt (- (* b_2 b_2) (* a c)))
1.2b	(- (* b_2 b_2) (* a c))
0.4b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

Slowest

102.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
50.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(- (* b_2 b_2) (* a c))

series406.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

126.0ms	(sqrt (- (* b_2 b_2) (* a c)))
119.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
104.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
56.0ms	(- (* b_2 b_2) (* a c))

simplify4.4s

Counts

73 → 100

Calls

73 calls:

Slowest

463.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
374.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
289.0ms	(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))
289.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
263.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize35.0ms

Local error

Found 4 expressions with local error:

20.2b	(sqrt (- (* b_2 b_2) (* a c)))
20.2b	(sqrt (- (* b_2 b_2) (* a c)))
1.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (* b_2 b_2) (* a c))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

Slowest

14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series270.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

96.0ms	(sqrt (- (* b_2 b_2) (* a c)))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))
52.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(- (* b_2 b_2) (* a c))

simplify2.9s

Counts

28 → 70

Calls

28 calls:

Slowest

716.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
377.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
302.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
271.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
214.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune871.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize51.0ms

Local error

Found 4 expressions with local error:

20.2b	(sqrt (- (* b_2 b_2) (* a c)))
20.2b	(sqrt (- (* b_2 b_2) (* a c)))
20.2b	(sqrt (- (* b_2 b_2) (* a c)))
1.2b	(- (* b_2 b_2) (* a c))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 61

Calls

4 calls:

Slowest

15.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(sqrt (- (* b_2 b_2) (* a c)))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))
51.0ms	(- (* b_2 b_2) (* a c))

simplify3.2s

Counts

34 → 73

Calls

34 calls:

Slowest

340.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
337.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
313.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
267.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
241.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

localize74.0ms

Local error

Found 4 expressions with local error:

21.0b	(cbrt (- (* b_2 b_2) (* a c)))
21.0b	(cbrt (- (* b_2 b_2) (* a c)))
20.2b	(sqrt (- (* b_2 b_2) (* a c)))
6.5b	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`cbrt-div` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 57

Calls

4 calls:

Slowest

25.0ms	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
6.0ms	(cbrt (- (* b_2 b_2) (* a c)))
5.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
125.0ms	(cbrt (- (* b_2 b_2) (* a c)))
97.0ms	(cbrt (- (* b_2 b_2) (* a c)))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.1s

Counts

30 → 69

Calls

30 calls:

Slowest

454.0ms	(- (exp (* 1/3 (+ (log a) (+ (log -1) (log c))))) (* 1/3 (* (pow b_2 2) (exp (* 1/3 (- (log -1) (+ (* 2 (log a)) (* 2 (log c)))))))))
382.0ms	(- (exp (* 1/3 (+ (log a) (+ (log -1) (log c))))) (* 1/3 (* (pow b_2 2) (exp (* 1/3 (- (log -1) (+ (* 2 (log a)) (* 2 (log c)))))))))
368.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
316.0ms	(cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
306.0ms	(cbrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))

prune1.2s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.6b

regimes351.0ms

Accuracy

78.2% (6.0b remaining)

Error of 11.6b against oracle of 5.6b and baseline of 33.3b

bsearch194.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.2s	5901×	body	80	valid
934.0ms	1077×	body	2560	valid
667.0ms	879×	body	1280	valid
382.0ms	2886×	body	80	nan
198.0ms	471×	body	640	valid
78.0ms	95×	body	5120	valid
71.0ms	217×	body	320	valid
47.0ms	113×	body	160	valid